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3 years ago

Simplify the expression by combining like terms, if possible. 4a^2+2a+4a^2-5

Mathematics

1 answer:

Sati [7]3 years ago

6 0

Answer:

8a2+2a−5

Step-by-step explanation:

The 2 next to 8a means power of 2. Just wanted to clarify.

Hope this helps! Have a nice night (^-^)

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A worker drags a box of mass 50 kg across a horizontal floor. The worker attaches a rope to the box and pulls on the rope so tha

Arlecino [84]

Answer:

A) $F=\displaystyle{\frac{m(a+ \mu g)}{\cos(\alpha) -\mu \sin(\alpha)} }$ with $a = \frac{2\Delta x}{t^2}$

B) The magnitude of the pulling force is 24 % of the magnitude of the gravitational force acting on the box

Step-by-step explanation:

A) The forces acting on the box are the pulling force that the worker exerts on the rope, the friction, the normal force, and the gravitational force. See the attached diagram. Since the pulling force on the rope makes an angle with the horizontal, this will have components in the x and y-axis (see diagram).

In the y-axis, the box does not move, therefore:

$\sum_{y} F = 0\\F\sin(\alpha) + N - F_g = 0\\N = F_g - F\sin(\alpha)\\N = mg - F\sin(\alpha)$ (1)

where $\alpha$ is the given angle of the rope with the horizontal.

In the x-axis, the box moves with an acceleration $a$ that can be calculated as a function of the given displacement and time interval as:

$a = \frac{2\Delta x}{t^2}$ and the force equation is:

$\sum_{x} F = ma\\F\cos(\alpha) -f =ma\\F\cos(\alpha) - \mu N = ma$

now substituting $N$ from equation (1):

$F\cos(\alpha) - \mu N = ma\\F\cos(\alpha) - \mu (mg - F\sin(\alpha))=ma\\F\cos(\alpha) - \mu mg -\mu F\sin(\alpha)=ma\\F\cos(\alpha) -\mu F\sin(\alpha)=ma+ \mu mg\\F(\cos(\alpha) -\mu \sin(\alpha))=ma+ \mu mg\\\boxed{F=\frac{m(a+ \mu g)}{\cos(\alpha) -\mu \sin(\alpha)}}$

and putting the expression for the acceleration:

$\boxed{F=\frac{m \frac{2\Delta x}{t^2}+ \mu mg}{\cos(\alpha) -\mu \sin(\alpha)}}$ (2)

which is the requested expression

B) Substituting the values in (2) and using $g=9.8\ \rm{ms^{-2}}$ :

$F=\frac{50 \cdot ( 0.762939+ 0.1\cdot \cdot 9.8)}{\cos(36.8^{\circ}) -0.1 \sin(36.8^{\circ})}\\F=\frac{87.147}{0.740829} \\F=11.634\ \rm{N}$

The gravitational force acting on the box is:

$F_g=mg=50\cdot9.8=490\ \rm{N}$

$F/F_g = (117.634/490)\cdot 100 = 24 \%$

Thus, the magnitude of the pulling force is 24 % of the magnitude of the gravitational force acting on the box.

8 0

4 years ago

Paul's budget for food is 30% of the budget he has for rent.

SpyIntel [72]

Paul's rent budget is <u>$750</u>, given that his food budget of $225, is 30 percent of his rent budget.

<h3> What are fractions?</h3>

Fractions are representation of quantities as a part of a certain quantity.

Written as <u>a/b</u>, read as <u>a by b</u>, and functions as <u>a divided by b</u>, represents a fraction showing a parts of b equal parts.

a is called the numerator, and b is called the denominator.

<h3>What are percentages?</h3>

Percentages are modified fractions where the whole quantity is represented by 100.

To convert a fraction into percentages we multiply it by 100, while to convert percentages to fraction divided by 100.

<h3>How to solve the question?</h3>

In the question, we are given that Paul's budget for food is 30% of the budget he has for rent.

We are asked if his budget for food is $225, what is his budget for rent.

We assume Paul's budget for rent to be $x.

We know that Paul's food's budget is 30 percent of his rent.

Hence, Paul's food budget = 30% of x.

or, Paul's budget for food = 30/100 * x {To convert percentages to fraction divided by 100}

But, we know that Paul's food budget is $225. Thus, we can show that:

225 = 30/100 * x,

or, x = (225*100)/30 = 750.

Thus, Paul's rent budget is <u>$750</u>, given that his food budget of $225, is 30 percent of his rent budget.

Learn more about percentages at

brainly.com/question/843074

#SPJ2

3 0

2 years ago

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Humihingi po ako sa inyo ng tulong po, sana matulungan nyo po ako dito☝

suter [353]

I Domitila get hungry :

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3 years ago

Matt can buy an 8-ounce jar of salsa for $2.79 or a 15-ounce jar of salsa for $5.54. Which jar has the best unit rate?

katrin [286]

Answer:

15 ounce

Step-by-step explanation:

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4 years ago

Can someone help me?

timama [110]

Answer:

Step-by-step explanation:

X = 152 -90 = 62 degree

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3 years ago