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Karo-lina-s [1.5K]

2 years ago

6

Find the area of a rectangle with the length of 1 3/4 foot and a width of 1 1/2 foot.

1 answer:

Stolb23 [73]2 years ago

4 0

To find the Area you need to use the formula L x W!! Anyways, You have to multiply the Length x the width. Your Length is 1 3/4 and your width is 1 1/2. So 1 3/4 x 1 1/2 is 2 5/8!!

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Solve for the zeros of the quadratic function f(x) = 9x² + 6x + 1.

Nezavi [6.7K]

Answer:

$\large\boxed{x=-\dfrac{1}{3}}$

Step-by-step explanation:

$f(x)=9x^2+6x+1\\\\\text{The zeros are for}\ f(x)=0\\\\9x^2+6x+1=0\\\\9x^2+3x+3x+1=0\\\\3x(3x+1)+1(3x+1)=0\\\\(3x+1)(3x+1)=0\\\\(3x+1)^2=0\iff3x+1=0\qquad\text{subtract 1 from both sides}\\\\3x=-1\qquad\text{divide both sides by 3}\\\\x=-\dfrac{1}{3}$

8 0

3 years ago

A trough has ends shaped like isosceles triangles, with width 5 m and height 7 m, and the trough is 12 m long. Water is being pu

Svet_ta [14]

Answer:

$\dfrac{dh}{dt}=21 \text{m/min}$

the rate of change of height when the water is 1 meter deep is 21 m/min

Step-by-step explanation:

First we need to find the volume of the trough given its dimensions and shape: (it has a prism shape so we can directly use that formula OR we can multiply the area of its triangular face with the length of the trough)

$V = \dfrac{1}{2}(bh)\times L$

here L is a constant since that won't change as the water is being filled in the trough, however 'b' and 'h' will be changing. The equation has two independent variables and we need to convert this equation so it is only dependent on 'h' (the height of the water).

As its an isosceles triangle we can find a relationship between b and h. the ratio between the b and h will be always be the same:

$\dfrac{b}{h} = \dfrac{5}{7}$

$b=\dfrac{5}{7}h$ this can be substituted back in the volume equation

$V = \dfrac{5}{14}h^2L$

the rate of the water flowing in is:

$\dfrac{dV}{dt} = 6$

The question is asking for the rate of change of height (m/min) hence that can be denoted as: $\frac{dh}{dt}$

Using the chainrule:

$\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}$

the only thing missing in this equation is dh/dV which can be easily obtained by differentiating the volume equation with respect to h

$V = \dfrac{5}{14}h^2L$

$\dfrac{dV}{dh} = \dfrac{5}{7}hL$

reciprocating

$\dfrac{dh}{dV} = \dfrac{7}{5hL}$

plugging everything in the chain rule equation:

$\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}$

$\dfrac{dh}{dt}=\dfrac{7}{5hL}\times 6$

$\dfrac{dh}{dt}=\dfrac{42}{5hL}$

L = 12, and h = 1 (when the water is 1m deep)

$\dfrac{dh}{dt}=\dfrac{42}{5(1)(12)}$

$\dfrac{dh}{dt}=21 \text{m/min}$

the rate of change of height when the water is 1 meter deep is 21 m/min

6 0

3 years ago

Read 2 more answers

If f(x) = x is changed to g(x) = -f(x + 3) + 2, how is the graph transformed?

Dvinal [7]

Answer:

f(x) is flipped, and each point is moved 3 units to the left and 2 units up

Step-by-step explanation:

8 0

3 years ago

Find the missing lengths!!!!!!!

Katen [24]

Answer:

13

Step-by-step explanation:

It is a square so the length of 1 side = $\sqrt{169}$ = 13

5 0

2 years ago

Ali spends 30% monthly income on food articles, 40% of the remaining on conveyance and clothes and saves 50% of the remaining. I

Romashka [77]

Ali saves Rs 2576 every month

Step-by-step explanation:

Step 1: Given Ali's monthly salary = Rs 18400. Calculate the amount spent on food articles

Amount spent on food = 30% of 18400 = 30/100 × 18400 = Rs 5520

Step 2: Find the remaining amount.

Remaining amount = 18400 - 5520 = Rs 12880

Step 3: Find amount spend on conveyance and clothes

Amount spent on conveyance and clothes = 40% of 12880

= 40/100 × 12880 = Rs 5152

Step 4: Find his monthly savings.

Monthly savings = 50% of 5152 = 50/100 × 5152 = Rs 2576

5 0

3 years ago

Read 2 more answers