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3 years ago

6

Find three positive numbers a, b and c such that 2 times a plus 14 times b plus 16 times c equals 176, and such that the product

of a, b and c is a maximum.

1 answer:

Juli2301 [7.4K]3 years ago

5 0

33333333333333333333333333

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Paul is spreading grass seed on an area of his lawn that is 9 feet wide and 10 feet long. A bag of grass seed covers 15 square f

aksik [14]

Area of the field should be 9*10 = 90 square feet.
a bag of grass seeds cover 15 square feet.
so if you need to know how many bags should be used, then,
Total area of field/ area covered by 1 bag of grass seeds.
= 90/15 = 6 bags
he needs to use 6 bags of grass seeds to cover the whole field.
I don't think there are any 'hidden' questions, though you can consider the 2nd part of the question I guess. (how many bags of seed will Paul...)

3 0

3 years ago

3p + 2q = 14<br> 10p + 6q = 44<br> What is p and what is q

Airida [17]

Answer:

p = 2 ; q = 4

Step-by-step explanation:

Given tbe equation :

3p + 2q = 14 - - - (1)

10p + 6q = 44 - - -(2)

What is p and what is q

This is a simultaneous equation ; using elimination method :

Multiply (1) by 6 and (2) by 2

18p + 12q = 84 - - - - (3)

20p + 12q = 88 - - - (4)

Subtract (3) and (4)

-2p = - 4

p = 4/2

p = 2

Put p = 2 in (1)

3p + 2q = 14

3(2) + 2q = 14

6 + 2q = 14

2q = 14 - 6

2q = 8

q = 8/2

q = 4

p = 2 ; q = 4

4 0

3 years ago

An athlete knows that when she jogs along her neighborhood greenway, she can complete the route in 10 minutes. It takes 20 minu

IgorLugansk [536]

Answer:

10 miles per hour.

Step-by-step explanation:

Let x represent athlete's walking speed.

We have been given that her jogging rate is 5 mph faster than her walking rate, so athlete's jogging speed would be $x+5$ miles per hour.

$\text{Distance}=\text{Rate}\cdot \text{Time}$

10 minutes = 1/6 hour.

20 minutes = 1/3 hour

While walking, we will get $D_{\text{walking}}=x\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{3}\text{hour}$

$D_{\text{walking}}=\frac{x}{3}$

While jogging, we will get $D_{\text{jogging}}=(x+5)\frac{\text{miles}}{\text{hour}}\cdot \frac{1}{6}\text{hour}$

$D_{\text{jogging}}= \frac{(x+5)}{6}$

Since athlete is covering same distance while walking and jogging, so we can equate both expressions as:

$\frac{x}{3}=\frac{x+5}{6}$

Cross multiply:

$6x=3x+15$

$6x-3x=15$

$3x=15$

$\frac{3x}{3}=\frac{15}{3}\\\\x=5$

Therefore, athlete's walking speed is 5 miles per hour.

Jogging speed: $x+5\Rightarrow 5+5=10$

Therefore, athlete's jogging speed is 10 miles per hour.

3 0

3 years ago

Y varies directly as x. Y=28 when x=2. Find y when x=12

Tatiana [17]

Answer:

Y=168

Step-by-step explanation:

Y varies directly as X

Y=kx

K is a constant

28=k2

K=28/2 =14

Y=14x

Y=14×12

Y=168

4 0

2 years ago

A brand new filled jar of salsa is 11 cm tall and a has a radius of 6 cm. Kelly eats some of the salsa and the salsa in the jar

Sonbull [250]

Before we begin please note that a jar is always cylindrical in shape if not mentioned otherwise. Thus, we will take a cylindrical jar in this case.

Since Kelly eats some of the salsa and the salsa in the jar is now 6 cm high, we know that Kelly ate the amount of Salsa whose volume is missing from the jar.

To find the missing volume on the Salsa jar all that we need to do is to find the height of the missing volume which is given to us as h= 6 cm. We already know that the radius of the jar, r=6 cm. Thus, the amount of Salsa Kelly has eaten is:

$V=\pi(6)^2\times 6\approx678.6\approx679$ $cm^3$

Thus, the third option is the correct answer

8 0

3 years ago

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