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3 years ago

a certain recipe calls for 3 2/3 cups of sugar. If the recipe is to be doubled how much sugar should be used?

Mathematics

1 answer:

Zarrin [17]3 years ago

7 0

Answer:7 1/3

Step-by-step explanation: 3 ×2= 6 2/3 × 2= 4/3 or 1 1/3 so it would be 7 1/3

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Find the average rate of change of the function over the given interval

sattari [20]

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------\\\\$

$\bf h(t)=cot(t)\implies h(t)=\cfrac{cos(t)}{sin(t)}\quad 
\begin{cases}
t_1=\frac{\pi }{4}\\
t_2=\frac{3\pi }{4}
\end{cases}\implies \cfrac{h\left( \frac{3\pi }{4} \right)-h\left( \frac{\pi }{4} \right)}{\frac{3\pi }{4}-\frac{\pi }{4}}
\\\\\\$

$\bf \cfrac{\frac{cos\left( \frac{3\pi }{4} \right)}{sin\left( \frac{3\pi }{4} \right)}-\frac{cos\left( \frac{\pi }{4} \right)}{sin\left( \frac{\pi }{4} \right)}}{\frac{\pi }{2}}\implies \cfrac{-1-1}{\frac{\pi }{2}}\implies \cfrac{-2}{\frac{\pi }{2}}\implies -\cfrac{4}{\pi }\\\\\\
-------------------------------\\\\$

$\bf h(t)=cot(t)\implies h(t)=\cfrac{cos(t)}{sin(t)}\quad 
\begin{cases}
t_1=\frac{\pi }{3}\\
t_2=\frac{3\pi }{2}
\end{cases}\implies \cfrac{h\left( \frac{3\pi }{2} \right)-h\left( \frac{\pi }{3} \right)}{\frac{3\pi }{2}-\frac{\pi }{3}}
\\\\\\$

$\bf \cfrac{\frac{cos\left( \frac{3\pi }{2} \right)}{sin\left( \frac{3\pi }{2} \right)}-\frac{cos\left( \frac{\pi }{3} \right)}{sin\left( \frac{\pi }{3} \right)}}{\frac{9\pi -2\pi }{6}}\implies \cfrac{\frac{0}{-1}-\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}}{\frac{7\pi }{6}}\implies\cfrac{-\frac{1}{\sqrt{3}}}{\frac{7\pi }{6}}\implies -\cfrac{\sqrt{3}}{3}\cdot \cfrac{6}{7\pi }
\\\\\\
-\cfrac{2\sqrt{3}}{7\pi }$

8 0

3 years ago

S+(4×-7 smplify by combining like terms

zvonat [6]

Answer:

s+4x-7

Step-by-step explanation:

Remove parentheses.

7 0

3 years ago

Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?

iren2701 [21]

Answer: f(x) = –3x + 14

Step-by-step explanation:

The point slope form of an equation is expressed as

y - y1 = m(x - x1)

The given equation is

y + 1 = –3(x – 5)

Comparing with the point slope equation,

y1 = - 1

Slope, m = - 3

x1 = 5

The equation of a straight line can also take the slope intercept form,

y = mx + c

Where

m is the slope(change in y /change in x)

c represents the intercept.

We would determine the intercept by substituting x = 5 , y = -1 , m = - 3, into y = mx + c. It becomes

- 1 = - 3 × 5 + c

- 1 = -15 + c

c = - 1 + 15 = 14

The equation becomes

y = -3x + 14

7 0

3 years ago

6 of 6

SashulF [63]

Answer:

3.2 km/h

Step-by-step explanation:

1. Approach

The average speed is the rate at which one travels. It can be found by diving the total distance traveled over the total time it took to cover that distance. In essence, the following formula can be used to find the average speed:

$\frac{total\ distance}{total\ time}=average\ speed$

In this situation, one is asked to find the difference between two people's average speed. One is given the following information:

Lena: 24 miles 1.5 hours

Ras: 36km 1 hour 15 minutes

First, convert all of the numbers into the correct units (km) and (hours). Then find the average speed for each person. Finally, subtract the smaller speed from the larger speed to find the difference in the average speeds.

1. Find Lena's average speed

The problem asks one to find the average speed in the units (km/h). However, the distance Lena covered is given in (miles). Therefore, one has to multiply it by the conversion factor (1.6) in order to convert it from (miles) to (km).

24miles * 1.6 = 38.4

Now find the average speed by using the formula:

$\frac{total\ distance}{total\ time}=average\ speed$

Substitute,

$\frac{38.4}{1.5}\\\\=25.6$

2. Find Ras's average speed

Use a similar approach to work out Ras's average speed, as was used to find Lena's average speed. Since Ras's time spent is given in both hours and minutes, one must convert it to just minutes. There are (60) minutes in an hour, thus, one can rewrite the number as the following:

$1\ hour \ \ 15\ minutes= 1 \frac{15}{60}\ hours = \frac{75}{60}\ hours$

Now find the average speed:

$\frac{total\ distance}{total\ time}=average\ speed$

Substitute,

$\frac{36}{\frac{75}{60}}\\\\=28.8$

3. Find the difference between the speeds

Since Ras's speed is greater, subtract Lena's speed from Ras's speed.

Ras - Lena

= 28.8 - 25.6

= 3.2

6 0

2 years ago

Solve for b. 5/b = 45/36 b = ?

nikitadnepr [17]

Answer:

b=4

Step-by-step explanation:

Format rewrite:

Solve for 'b', when $\frac{5}{b} =\frac{45}{36}\\\\\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c\\\\5\cdot \:36=b\cdot \:45\\180=b\cdot \:45\\\\divide(45)\\\\\\\\\\b=4$

Hoped this help ya

<3

red

4 0

3 years ago