A pail holds 2 3/4 gallons of water. How much is this in cups?

Mathematics

1 answer:

Sever21 [200]3 years ago

3 0

There are 16 cups in 1 gallon:
16 x 2.75 = 44 cups

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Y'all I am struggling Use the following functions to find each value below. f(x)=5x; g(x)=−2x+1; h(x)=x2+6x+8

Anni [7]

Answer:

see below the first three problems

Step-by-step explanation:

f(g(-2))

First, find g(-2) using function g(x). Then use that value as input for function f(x).

g(x) = -2x + 1

g(-2) = -2(-2) + 1

g(-2) = 5

f(x) = 5x

f(5) = 5(5)

f(5) = 25

f(g(-2)) = 25

g(h(3))

First, find h(3) using function h(x). Then use that value as input for function g(x).

h(x) = x^2 + 6x + 8

h(3) = 3^2 + 6(3) + 8 = 9 + 18 + 8

h(3) = 35

g(x) = -2x + 1

g(35) = -2(35) + 1 = -70 + 1

g(35) = -69

g(h(3)) = -69

f(g(3a))

First, find g(3a) using function g(x). Then use that value as input for function f(x).

g(x) = -2x + 1

g(3a) = -2(3a) + 1

g(3a) = -6a + 1

f(x) = 5x

f(-6a + 1) = 5(-6a + 1)

f(-6a + 1) = -30a + 5

f(g(3a)) = -30a + 5

5 0

3 years ago

Two sides of a triangle are 6 m and 10 m in length and the angle between them is increasing at a rate of 0.06 rad/s. find the ra

Soloha48 [4]

Since this problem talks about rates of change, then the concept of calculus is very useful. But first, let's find at least two equations in order to solve this system. The first one is the area of a triangle written as

A = 1/2 ab sin θ, where a and b are the sides that from the angle θ. So, we substitute a=6 and b=10. That makes it:
A = 1/2 (6)(10)sin θ = 30 sin θ

Now, you differentiate implicitly (both sides simultaneously) with respect to time.

dA/dt = 30 cosθ (dθ/dt)

We replace dθ/dt = 0.06 rad/s, as mentioned in the problem. Then, the rate of change of the area of the triangle when θ = π/3 rad with respect to time is

dA/dt = 30cos(π/3) (0.06)
dA/dt = 1.8 m²/s

Therefore, the rate of change of the area of the triangle is 1.8 m² per second.

8 0

3 years ago

Number 6. I have no idea how to do this because the question doesn’t give enough information

Savatey [412]

${13}^{2} = {5}^{2} \times {b}^{2} \\ 169 = 25 \times {b}^{2} \\ 165 - 25 = {b}^{2} \\ 144 = {b}^{2} \\ \sqrt{ {b}^{2} } = \sqrt{144} \\ b = 12$